Question

a rectangular park is 105 yards long and 60 yards wide. give the length and width of another rectangular park that has the same perimeter but a smaller area. width = yards length = yards

Explanation:

Step1: Calculate the perimeter of the original park

The formula for the perimeter of a rectangle is \(P = 2(l + w)\). For the given park with \(l = 105\) yards and \(w = 60\) yards, \(P=2(105 + 60)=2\times165 = 330\) yards.

Step2: Calculate the area of the original park

The formula for the area of a rectangle is \(A=l\times w\). So, \(A = 105\times60=6300\) square - yards.

Step3: Find another rectangle with the same perimeter

Let the new length be \(l_1\) and new width be \(w_1\). Since \(P = 2(l_1+w_1)=330\), then \(l_1 + w_1=165\), so \(l_1=165 - w_1\).
The area of the new rectangle \(A_1=l_1\times w_1=(165 - w_1)\times w_1=165w_1 - w_1^{2}\).
We can try values. Let's take \(w_1 = 30\) yards. Then \(l_1=165 - 30=135\) yards.

Step4: Calculate the area of the new rectangle

\(A_1=135\times30 = 4050\) square - yards. Since \(4050<6300\)

Answer:

width = 30 yards, length = 135 yards